This dissertation investigates the motion of a levitated droplet experimentally and analytically against the Marangoni flow in an immiscible outer fluid at higher speeds than is possible currently. Based on our earlier experiments, when a droplet is released from a height of 1.5 – 4 times its diameter from the liquid surface, it can overcome the impact and stay levitated at the liquid-air interface due to the existence of an air gap between the droplet and the liquid film. In order to explain this behavior of droplet traveling against the counter-current motion, we propose a simple approach: first, the Marangoni convection inside the thin film is considered without the droplet floating on the surface. By using a level-set method and solving the Navier-Stokes equation, the free surface velocity and deformation are calculated. Then, these quantities are used to solve for droplet velocity and drag coefficient simultaneously using a force balance. In order to compare the simulation results, experiments with levitated water droplets on an immiscible carrier liquid, FC-43, were conducted for various temperature gradients, and droplet velocities were measured at different locations using high-speed imaging. The experimental results are in good agreement with the developed theoretical model. For a Reynolds number range of 2-32, it is shown that the drag coefficients are up to 66% higher than those for the fully immersed sphere at the same Reynolds numbers. A correlation is proposed to calculate the drag coefficient of levitated droplets for various temperature drops across the channel. For the first time, it is shown that it is possible to realize the natural coalescence of droplets through Marangoni effect without any external stimulation, and deliver the coalesced droplet to a certain destination through the use of surface tension gradients. The effects of the various shapes and sizes upon collision are studied. Regions of coalescence and stretching separation of colliding droplets are delineated based on Weber number and impact number. The existence of the transition line between coalescence and stretching separation in this passive mode of transport is similar to what was observed in the literature for forced coalescence at significantly higher Weber numbers. It is also found that a thermocapillary environment improves the mixing process. In order to illustrate and quantify the mixing phenomenon, the dispensed droplets were made of potassium hydroxide and phenolphthalein which is used as a pH indicator. The experiments show the possibility to reach mixing rates as high as 74% within 120 ms. This study offers new insight to thermo-coalescence and demonstrates how natural coalescence could be used to transport, mix and collect biochemical assays more efficiently. The results of this research can be engineered to enhance the performance of self-cleaning surfaces and micro-total analysis systems (µTAS), where sample transport, filtration, chemical reactions, separation and detection are of great interest.


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Graduation Date





Kumar, Ranganathan


Doctor of Philosophy (Ph.D.)


College of Engineering and Computer Science


Mechanical and Aerospace Engineering

Degree Program

Mechanical Engineering









Release Date

February 2016

Length of Campus-only Access


Access Status

Doctoral Dissertation (Open Access)